Ok...
The image you posted is indeed 600x600px but its at a resolution of 72ppi.
This means if you were to PRINT that it would give you an image approx 8" square.
Your NEW document is 11" x 17" (I presume you mean inches?) @ 300ppi.
This gives you a document 3300x5100px.
Fitting the original 600x600px image into that new document gives you this:
[ATTACH]53223[/ATTACH]
When you 'resized' I assume you transformed the image up to a size nearer the document size.
Transforming [scale] is actualy 're-sampling' the image, and uses the algorithm you choose to process the pixels.(Bilinear, Bicubic, etc)
ANY transform [scale] will change what you perceive as 'quality'. Re-sampling UP has to ADD pixels, re-sampling DOWN removes pixels.
Re-sampling should be avoided at all costs but if it has to be done then re-sampling DOWN is better as no pixels have to be interpreted....all the information needed is already in the image.
What you have done here, assuming you have made that image fit the width of your new document, is to re-sample the image by OVER 600%....!!!!!!
This is not good.
What you could do is make your NEW document the same 72ppi as the image....you would then not have to transform the image so much to fit...
[ATTACH]53224[/ATTACH]
The problem here though is that you may need more than 72ppi when you send it for printing....your printer (Of the human kind) may require a minimum of say 300ppi.
In this case you have no alternative but to scale the image by over 600% to fit and live with the results....good or bad.
You can use the VIEW > 'Print Size' option in PS which will show you the image at its PRINT size but that does require entering correct settings in the PS preferences.
If you have not already done this I can go through it with you.
This will give you a 'rough' idea of how it look when printed but you have to remember you are viewing it on a DIGITAL device....your monitor....which has its own 'resolution', not on paper which will have a resolution dependant on the printer (As in the mechanical kind) settings.....(Its DPI setting)
Thats probably confused you even more but its a simple case of there are only so many pixels in an image.... the 'resolution' you set will determine how big that image will be printed.
What you gain on the swings you lose on the roundabouts.
Regards.
MrTom.